Gnomonic Number

Author

Eric W. Weisstein
September 6, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/GnomonicNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GnomonicNumber.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Generating Function

Series[((-1+3 x)/(((-1+x))^2)),{x,0,10}]

Series[1+((-1+3 x)/(((-1+x))^2)),{x,0,10}]

(n^2)-(((n-1))^2)

Sum[((n^2)-(((n-1))^2))(x^n),{n,0,∞}]

GeneratingFunction[(n^2)-(((n-1))^2),n,x]

SeriesCoefficient[((-1+3 x)/(((-1+x))^2)),{x,0,n}]

2 n-1

Sum[(2n-1)(x^n),{n,0,∞}]

GeneratingFunction[2n-1,n,x]

SeriesCoefficient[((-1+3 x)/(((-1+x))^2)),{x,0,n}]

Figure

square[{x_,y_}]:=Module[{h=1/2},
Line[{{x-h,y-h},{x+h,y-h},{x+h,y+h},{x-h,y+h},{x-h,y-h}}]
]

Gnomon[n_,pos_:{0,0}]:=Module[{x},
{
Table[square[pos+{x,0}],{x,0,n-1}],
Table[square[pos+{0,x}],{x,1,n-1}]
}
]

e=.1;
Show[GraphicsArray[
Table[Graphics[Gnomon[n],PlotRange->{{-1/2-e,5-1/2+e},{-1/2-e,5-1/2+e}},AspectRatio->Automatic],{n,5}]]]